Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)



Periods of automorphic forms

Authors: Hervé Jacquet, Erez Lapid and Jonathan Rogawski
Journal: J. Amer. Math. Soc. 12 (1999), 173-240
MSC (1991): Primary 11F55, 11F70, 11F72
MathSciNet review: 1625060
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Abstract: Let $E/F$ be a quadratic extension of number fields and $G= \operatorname{Res}_{E/F}H$, where $H$ is a reductive group over $F$. We define the integral (in general, non-convergent) of an automorphic form on $G$ over $H(F)\backslash H(\mathbb A)^1$ via regularization. This regularized integral is used to derive a formula for the integral over $H(F)\backslash H(\mathbb A)^1$ of a truncated Eisenstein series on $G$. More explicit results are obtained in the case $H=GL(n)$. These results will find applications in the expansion of the spectral side of the relative trace formula.

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Additional Information

Hervé Jacquet
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027

Erez Lapid
Affiliation: Department of Mathematics, Weizmann Institute, Rehovot, Israel

Jonathan Rogawski
Affiliation: Department of Mathematics, Hebrew University, Jerusalem, Israel
Address at time of publication: Department of Mathematics, University of California, Los Angeles, California 90095

Received by editor(s): October 14, 1997
Received by editor(s) in revised form: May 14, 1998
Additional Notes: The first author was partially supported by NSF Grant 9619766.
The third author was partially supported by NSF Grant 9401466.
Article copyright: © Copyright 1999 American Mathematical Society